Sulfur Trioxide is a neutral molecule because it has the same amount of electrons as protons. Sulfite has two extra electrons though making it an ion because it has a charge, specifically an anion because it has a negative charge. Molecules can gain and lose electrons through oxidation-reduction reactions (a transfer of electrons from one molecule to another).
So yes they both have the same atoms SO3 but they have different chemical properties because having more electrons is probably going to make sulfite (SO3 2-) more reactive with other molecules and elements. They are different chemicals with different properties. More electrons does not necessarily mean the chemical is more reactive either, it totally depends on the chemical and what its most stable state is.